# Optimal production schedule

I need help in solving this linear programming model, specifically in identifying the different constraints for the problem.

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The Goliath Tool and Machine Shop produces a single product consisting of three sub-components that are assembled to form the product. The three components are manufactured in an operation involving two lathes and three presses. The production time for each machine for the three components is as follows:

(see chart in the attached file)

The shop splits the lathe workload evenly between the two lathes, and the press workload evenly among the three presses. Additionally, the firm wishes to produce quantities of components that will balance the daily loading among lathes and presses so that, on average, no machine is operated more than one hour per day longer than any other machine. Each machine is available for eight hours per day. The shop wishes to produce the maximum quantity of assembled products each day, without partial assemblies (in-process inventories).

a. Formulate a linear programming model that can be used to determine the daily production schedule.

b. Determine the optimal production schedule using the Management Scientist software.

c. The production policies established by Goliath are relatively restrictive. If the company relaxed either its machine balancing requirement or its restriction on in-process inventory, determine which would have the greatest impact on production output. Determine the impact if both requirements were relaxed.

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#### Solution Summary

This shows how to formulate a linear programming model for a given situation and determine optimal production schedule.